Two commercial aircraft enroute from BWI to Los Angeles are flying at the same l
ID: 3220348 • Letter: T
Question
Two commercial aircraft enroute from BWI to Los Angeles are flying at the same lateral position (latitude and longitude) but at different altitudes. The altitude of aircraft 1 has a mean of 8.3 km and a standard deviation of 225 m. The altitude of aircraft 2 has a mean of 9.5 km and a standard deviation of 125 m. The altitudes of each aircraft can be viewed as independent random variables, but we do not know what distributions they follow.
8. Two commercial aircraft enroute from BWI to Los Angeles are flying at the same lateral position (latitude and longitude but at different altitudes. The altitude of aircraft 1 has a mean of 8.3 km and a standard deviation of 225 altitude of aircraft has of 9.5 km a standard deviation of 125 m. The altitudes of each aircraft can be viewed as independent random variables but we do not know what distributions they follow (a) What is the mean and standard deviation of the vertical distance between the two aircraft? ENME392 Spring 2017, University of Maryland (b) Assuming that the altitudes both follow normal distributions, what is the probability that the two aircraft are within 700 m of each other? (c Assuming that the altitudes both follow uniform distributions, what is the probability that the two aircraft are within 700 m of each other?Explanation / Answer
Aircraft 1
Mean = 8.3 km
sd = 225m = 0.225 km
variance = 0.0506 km
Aircraft 2
mean = 9.5km
sd = 125m = 0.125km
variance = 0.01562
a)
The mean of their height difference = 9.5 - 8.3 = 1.2
The difference of their variance = 0.035005
SD of their height difference = root( 0.035005) = 0.18721 km = 187.21 m
b)
for normal distribution
P(X < 700)
z = (700 - 1200 )/ 187.21 = -2.6707
calculating the probability by using the z value table
P(X<700) = 0.003785
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